Stability Analysis of Switched Linear Systems Under Persistent Dwell-Time Constraints

Persistent dwell-time (PDT) constraint is demonstrated to be powerful for modeling the dynamics of switched systems with nonuniform time-dependent scheduling constraints. However, the study of switched systems under PDT constraints presently struggles to provide nonconservative and convex stability conditions for stabilization. In this article, we present a novel concept called dictionary to precisely characterize PDT constraints. It outperforms the existing methods for PDT constraints, which undesirably involve inadmissible or redundant switching sequences. By building an advanced dictionary equivalent to any concerned PDT constraint, we develop a nonconservative stability criterion, which is further lifted to preserve convexity. Two numerical examples verify the derived theories.